Answer :

Given,

Also, ∠PST = ∠PRQ

⇒ Need to prove that PQR is an isosceles triangle.

⇒ If a line divides any two sides of a triangles in the same ratio then the same line is parallel to the third side.

⇒ Since, ST || QR

⇒ ∠PST = ∠PQR …………eq(1)

(Corresponding angles)

Also given ∠PST = ∠PRQ ……………eq(2)

From eq(1) and eq(2) we get

⇒ ∠PQR = ∠PRQ

Since, sides opposite to equal angles are equal

⇒ PR = PQ

∴ two sides of PQR is equal

PQR is an isosceles triangle

Hence proved.

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